Question

Question 1 (ii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Answer 1

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
Let $\frac{1}{\sqrt{x}}=p$ and $\frac{1}{\sqrt{y}}=q$, then the equations changes as below:
2p + 3q = 2 ... (i)
4p - 9q = -1 ... (ii)
Multiplying equation (i) by 3, we get
6p + 9q = 6 ... (iii)
Adding equation (ii) and (iii), we get
10p = 5
$p=\frac{1}{2}$ ....(iv)
Substituting the value of p in equation (i), we get
$2\times \frac{1}{2}+3q=2$
$\Rightarrow$3q = 1
$\Rightarrow$ $q=\frac{1}{3}$
Now,
$p=\frac{1}{\sqrt{x}}=\frac{1}{2}$
$\Rightarrow$ $\sqrt{x}=2$
$\Rightarrow$ $x=4$
and
$q=\frac{1}{\sqrt{y}}=\frac{1}{3}$
$\Rightarrow$ $\sqrt{y}=3$
$\Rightarrow$ y=9
Hence, x =4, y =9